2190edo: Difference between revisions

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~~The '''~~2190 ~~equal division''' divides the octave into 2190 equal parts of 0.5479 [[cent]]s each.~~ It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250.

{{EDO intro|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

=== Prime harmonics ===

=== ~~Miscellaneous properties~~ ===

=== Subsets and supersets ===

2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo|730]].

~~[[Category:Equal divisions of~~ the ~~octave|####]] ~~

4380edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.

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 {{Infobox ET}}
-The '''2190 equal division''' divides the octave into 2190 equal parts of 0.5479 [[cent]]s each. It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250.
+{{EDO intro|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.
 === Prime harmonics ===
 {{Harmonics in equal|2190|columns=11}}
-=== Miscellaneous properties ===
+=== Subsets and supersets ===
 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo|730]].
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.